A dualization approach to the ground state subspace classification of abelian higher gauge symmetry models

In the literature, abelian higher gauge symmetry models are shown to be valid in all finite dimensions and exhibit the characteristic behavior of symmetry protected topological phases models. While the ground state degeneracy and the entanglement entropy were thoroughly studied, the classification of the ground state space still remained obscure. Based on differentio-geometric approach and, anticipating the notation of the current paper, if C•,∂•Cis the chain complex associated to the geometrical content of these models, while G•,∂•Gis its symmetries counterpart, we show that the ground state space is classified by a H0(C, G) × H0(C, G) group, where H0(C, G) is the 0th cohomology and H0(C, G) is the corresponding 0th homology group with coefficients in the chain complex.